The Theory of Poker and Hold'em Strategy

15 Oct 2012

At Beaver Bar Camp X, I gave a talk on
the theory of poker and hold’em strategy. The slides were intended to skim the
iceberg of a professional poker player’s mindset. Though I’ll skim over what I
talked about here.

My Poker Career in a Nutshell

I first started playing online poker seriously on Pokerstars sometime during my
freshman year of college. Attracted by those endless promotions poker rooms
have, my first deposit into Pokerstars was $20. I read books, dove into forums,
did the math, paid for coaching videos, studied the game as if it were for my
computer science degree.

I began to beat the microstakes (2NL 6max) at a hot rate of 20 big blinds per
100 hands over several tens of thousands of hands. I played 4 tables at a time,
and played at least 4 hours a day. I moved onto 5NL on Full Tilt where I kept
beating the game, then went through a long downswing, though still up. I tried
my hand at a bit of heads-up; it wasn’t my thing. The US Department of Justice
eventually seized Poker Stars and Full Tilt on what was deemed “Black Friday”.
That was the end of that.

The Fundamental Theorem of Poker

We’ll jump right into Sklansky’s famous fundamental theorem of poker.

“Every time you play a hand differently from the way you would have played it
if you could see all your opponents’ cards, they gain; and every time you play
your hand the same way you would have played it if you could see all their
cards, they lose. Conversely, every time opponents play their hands differently
from the way they would have if they could see all your cards, you gain; and
every time they play their hands the same way they would have played if they
could see all your cards, you lose.” - David Sklansky

That makes sense. If we could see all of our opponent’s cards, we would play
perfectly and win. We can derive a mathematical expression for this by saying
that the more we deviate from playing as if we could see all of the cards, the
less benefit we gain. We can represent this most simply as Expected Value.

Expected Value

Expected value (EV) is basically how much you gain or lose on average on a
decision in the long run. Say we flip a coin where I get $1 if it’s Heads and
you get $2 if it’s Tails. My EV is -$.50 and your’s would be +$.50. Sure it’s
possible for me to get lucky and get a few tosses in my favor, but in the long
run it’s a good deal for you as you stand to gain positive EV, average $.50 per
flip.

Now let’s translate this into poker. Say we both go all-in with me holding
27-offsuit and you holding AA. It’s possible for me to get lucky and win the
hand, but it doesn’t mean you made the wrong decision. I have an 11% chance of
winning and my EV is -$1.22. It would clearly be a profitable
scenario for you, regardless of the outcome.

Making +EV decisions over a long enough period means a gain. This is the
fundamental idea of winning poker in the long run. Not mind-reading, not
psychology, not picking up tells.

Somewhat Advanced Math and Probability Stuff

With this established, I go into some concepts based on EV. I made these hands
up to best represent the concepts and present tougher decisions. Hey, I even
spent a long time doing the math, crunching numbers. These concepts include
pot odds, effective pot odds, implied odds, reverse implied odds, semibluffs,
and fold equity. Most often, one can apply pot odds to see whether they stand
to gain on calling a bet or raise, though they can apply to all decisions.

I won’t go into them on detail, but the main idea of all of these concepts is
to present situations where one could actually calculate the EV of their
possible actions to make an informed poker decision in practice.

I highly recommend taking a gander over these slides as they explain themselves
pretty well.

Hold’em Strategy

After I got some theory out of the went, I explained very basic hold’em
strategy. I went through what it means to play solid tight-aggressive (TAG)
poker including hand selection, positional awareness, general postflop play
tips. Then I went through some hand reading examples.

Different Playing Styles

When playing at a table, it’s important to identify the types of players at the
table as well as playing a solid playing style yourself. A good way to
categorize players online with the help of a poker heads-up-display (HUD) is by
their stats. Three stats that make it really easy to determine a player’s style
are Voluntary Put-in Pot % (VPIP), Preflop Raise % (PFR), and 3-bet % (3B).
VPIP is the percentage of hands they choose to play, PFR is the percentage of
hands they raise preflop (rather than simply call and limp), and 3B is the
percentage of hands they reraise.

A weak-tight player tends to have a very low VPIP, and a non-existent PFR. They
play very few hands (less than 10%), are not very aggressive, and fold
easily.

A loose-passive player has a high VPIP (more than 28%), and also a small PFR.
They play a lot of hands and aren’t very aggressive with them. Rather than bet
and raise, they will call with marginal hands or even nothing.

A tight-aggressive player has a low, but focused VPIP (13-18%) and a large PFR
(usually around the same as their VPIP). They choose +EV hands to play and play
them aggressively. They don’t limp preflop and usually always open the pot with
a raise. This is an extremely solid style of poker and most poker players that
play for living employ either this style or loose-aggressive.

A loose-aggressive player is pretty much the same as a tight-aggressive player,
but plays a bit more hands (20-26%).

Positional Awareness

Position is power. No, seriously. You have more EV playing hands in-position
than out-of-position. Good position is being in the seat that acts later in the
hand. The best positions are the button and cut-off (person in front of the
butter), and the worst positions are the small blind, big blind, and
under-the-gun (first to act preflop). Why you get more EV playing in-position
is because you know what your opponents choose to do before you have to
act. You thus have more information than your opponents in the hand. With
poker being a game of incomplete information, information is key.

For this reason, you should be extremely tight out-of-position, but you can
loosen up your hand selection in-position. I included a rough hand
selection chart weighted by position in the slides.

Cards in the Air

I go on to talk about post-flop play, poker
mindset (which I also
recommend skimming), and tools and resources. Really, I could write forever and
ever about the intracacies of poker and really hope the poker legislation in
the US loosens up in the future. It’s really a different game than what Casino
Royale 007 and what ESPN portrays. Having been a long spectator of these three
games, I can honestly say poker is a game similar to that of chess and
Starcraft. And like all other games, it’s more fun when you’re winning. So
perhaps at your next poker party, the words of David Sklansky will reverberate
in your head as you ponder that tough river call.